Question

consider the following lines.
$l_1: y = -\frac{6}{7}x - 7$
$l_2: y = \frac{7}{6}x + 1$
find the slope of $m_1$ of $l_1$ and the slope $m_2$ of $l_2$.
$m_1 = $
$m_2 = $
determine whether the lines are parallel, perpendicular, or neither.
parallel
perpendicular
neither

Explanation:

Step1: Identify slope of $L_1$

Lines in $y=mx+b$ form have slope $m$. For $L_1: y = -\frac{6}{7}x - 7$, $m_1 = -\frac{6}{7}$.

Step2: Identify slope of $L_2$

For $L_2: y = \frac{7}{6}x + 1$, $m_2 = \frac{7}{6}$.

Step3: Check parallel/perpendicular

Parallel lines have equal slopes; $-\frac{6}{7}
eq \frac{7}{6}$. Perpendicular lines have slopes with product $-1$:
$$m_1 \times m_2 = -\frac{6}{7} \times \frac{7}{6} = -1$$

Answer:

$m_1 = -\frac{6}{7}$
$m_2 = \frac{7}{6}$
perpendicular